“School of Mathematics”

Back to Papers Home
Back to Papers of School of Mathematics

Paper   IPM / M / 437
School of Mathematics
  Title:   Counting the centralizers of some finite groups
  Author(s):  A.R. Ashrafi
  Status:   Published
  Journal: Korean J. Comput. Appl. Math.
  No.:  1
  Vol.:  7
  Year:  2000
  Pages:   115-124
  Supported by:  IPM
For a finite group G, #Cent(G) denotes the number of centralizers of its elements. A group G is called n-centralizer if #Cent(G)=n, and primitive n-centralizer if #Cent(G) = #Cent([(G)/(Z(G))])=n.
In this paper we compute the number of distinct centralizers of some finite groups and investigate the structure of finite groups with exactly six distinct centralizers. We prove that if G is a 6-centralizer group then [(G)/(Z(G))] ≅ D8,A4,Z2×Z2×Z2 or Z2×Z2×Z2 ×Z2.

Download TeX format
back to top
scroll left or right